Tottenham Hotspur also got through but needed extra time to beat third division Port Vale 3-1 in the night's other fourth round tie.
Frank Lampard, Andriy Shevchenko, Michael Essien and Didier Drogba were on target for Chelsea as they roared back from Saturday's premier league defeat at Tottenham.
Although the competition offers a UEFA Cup place for the winners, most of the leading Premier League clubs have fielded weakened teams in recent seasons but Jose Mourinho wheeled out most of his big guns.
Villa too arrived at near full strength but the only team to take any league points from Stamford Bridge this season after their 1-1 September draw were overwhelmed by the London side, who dominated throughout.
Lampard headed them into the lead in the 32nd minute from a pinpoint Michael Ballack cross and Shevchenko found the net with a close-range header after another perfect delivery from Lampard in the 65th.
Chelsea were in complete command and got the third eight minutes from time when fullback Geremi crossed for Essien and Drogba rounded things off soon after when he seized on a blocked Salomon Kalou effort.
"When you get a setback like that (Tottenham defeat) you have to bounce back and we certainly bounced back," said Chelsea assistant manager Steve Clarke."
Seven times winners Liverpool got their goal in the fourth minute of first half injury time when Birmingham failed to clear a corner and Danish defender Daniel Agger lashed the loose ball into the roof of the net.
The added time was the result of lengthy treatment for Mohamed Sissoko after the midfielder suffered what appeared a dislocated shoulder after falling awkwardly in the 26th minute.
Maik Taylor saved a weakly-struck Craig Bellamy penalty in the 64th minute and the Welsh forward missed a sitter two minutes later.
Second division Birmingham, thrashed 7-0 by Liverpool on the same ground in the FA Cup last season, launched a furious late assault but could not find an equaliser.
Arsenal manager Arsene Wenger fielded a virtual reserve team at Goodison Park and they took a long time to get on top despite Everton having forward James McFadden sent off for dissent after 20 minutes.
Everton defended superbly but their marking was found wanting five minutes from time when Emmanuel Adebayor headed in a Mathieu Flamini cross.
Mart Poom, on for his Arsenal debut as a halftime substitute, then saved well to prevent Andy Johnson equalising within a minute.
Port Vale were dreaming of an upset when Leon Constantine struck his 11th goal of the season in a rare attack in the 64th minute.
Tottenham poured forward and levelled when Tom Huddlestone glanced in a header 10 minutes from time and the same player drove home the second in the first period of extra time.
Port Vale then ran out of steam and Jermain Defoe got a third for Spurs in the 107th minute.
On Tuesday Southend United, bottom of the second division, shocked holders Manchester United 1-0.
The draw for the quarter-finals takes place on Saturday with the final at Cardiff's Millennium Stadium on February 25.